Massimo Villata, a scientist from the Observatory of Turin in Italy, began the study with two major assumptions. First, he posited that both matter and antimatter have positive mass and energy density. Traditionally, the gravitational influence of a particle is determined solely by its mass. A positive mass value indicates that the particle will attract other particles gravitationally. Under Villata’s assumption, this applies to antiparticles as well. So under the influence of gravity, particles attract other particles and antiparticles attract other antiparticles. But what kind of force occurs between particles and antiparticles?

To resolve this question, Villata needed to institute the second assumption – that general relativity is CPT invariant. This means that the laws governing an ordinary matter particle in an ordinary field in spacetime can be applied equally well to scenarios in which charge (electric charge and internal quantum numbers), parity (spatial coordinates) and time are reversed, as they are for antimatter. When you reverse the equations of general relativity in charge, parity and time for either the particle or the field the particle is traveling in, the result is a change of sign in the gravity term, making it negative instead of positive and implying so-called antigravity between the two.

Villata cited the quaint example of an apple falling on Isaac Newton’s head. If an anti-apple falls on an anti-Earth, the two will attract and the anti-apple will hit anti-Newton on the head; however, an anti-apple cannot “fall” on regular old Earth, which is made of regular old matter. Instead, the anti-apple will fly away from Earth because of gravity’s change in sign. In other words, if general relativity is, in fact, CPT invariant, antigravity would cause particles and antiparticles to mutually repel. On a much larger scale, Villata claims that the universe is expanding because of this powerful repulsion between matter and antimatter

The gravitational behavior of antimatter is still unknown. While we may be confident that antimatter is self-attractive, the interaction between matter and antimatter might be either attractive or repulsive. We investigate this issue on theoretical grounds. Starting from the CPT invariance of physical laws, we transform matter into antimatter in the equations of both electrodynamics and gravitation. In the former case, the result is the well-known change of sign of the electric charge. In the latter, we find that the gravitational interaction between matter and antimatter is a mutual repulsion, i.e. antigravity appears as a prediction of general relativity when CPT is applied. This result supports cosmological models attempting to explain the Universe accelerated expansion in terms of a matter-antimatter repulsive interaction.

The gravitational repulsion would prevent the mutual annihilation of isolated and alternated systems of matter and antimatter. The location of antimatter could be identified with the well-known large-scale (tens of Mpc) voids observed in the distribution of galaxy clusters and superclusters. Indeed, Piran showed that these voids can originate from small negative fluctuations in the primordial density field, which (acting as if they have an effective negative gravitational mass) repel surrounding matter, and grow as the largest structures in the Universe. These new cosmological scenarios could eliminate the uncomfortable presence of an unidentified dark energy, and maybe also of cosmological dark matter, which, according to the Λ-CDM concordance model, would together represent more than the 95% of the Universe content.

If large-scale voids are the location of antimatter, why should we not observe anything there? There is more than one possible answer, which will be investigated elsewhere.